Question

For the graph, what is a reasonable constraint so that the function is at least 200?​

Answer 1

`0\leq x\leq 15`

Explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one

For the graph below, what should the domain be so that the function is at least 200? graph of y equals minus 2 times the square of x plus 30 times x plus 200

My answer:

Given the above information, we have:

`y=-2x^2+30x+200`

To make the function is at least 200, it means that:

`y=-2x^2+30x+200` ≥ 200

<=>
`-2x^2+30x` ≥ 0

<=> x(-2x+30) ≥ 0

This is the product of two numbers hence would be positive only if either both are positive or both are negative

• Case I: Both positive

x ≥ 0 and (-2x+30) ≥ 0

<=> 0 ≤ x ≤ 15

• Case II: Both negative

Then we get

`x\leq 0 and -2x+30\leq 0\\\\x\leq 0 and x\geq 15`

This is inconsistent as a value cannot be less than 0 and greater than 15

=> our correct answer is
`0\leq x\leq 15`

Hope it will find you well.